Optimal. Leaf size=25 \[ 4 \log (1-x)-14 \log (2-x)+11 \log (3-x) \]
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Rubi [A] time = 0.05, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {1612} \begin {gather*} 4 \log (1-x)-14 \log (2-x)+11 \log (3-x) \end {gather*}
Antiderivative was successfully verified.
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Rule 1612
Rubi steps
\begin {align*} \int \frac {4+3 x+x^2}{(-3+x) (-2+x) (-1+x)} \, dx &=\int \left (\frac {11}{-3+x}-\frac {14}{-2+x}+\frac {4}{-1+x}\right ) \, dx\\ &=4 \log (1-x)-14 \log (2-x)+11 \log (3-x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 19, normalized size = 0.76 \begin {gather*} 11 \log (x-3)-14 \log (x-2)+4 \log (x-1) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {4+3 x+x^2}{(-3+x) (-2+x) (-1+x)} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.13, size = 19, normalized size = 0.76 \begin {gather*} 4 \, \log \left (x - 1\right ) - 14 \, \log \left (x - 2\right ) + 11 \, \log \left (x - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.39, size = 22, normalized size = 0.88 \begin {gather*} 4 \, \log \left ({\left | x - 1 \right |}\right ) - 14 \, \log \left ({\left | x - 2 \right |}\right ) + 11 \, \log \left ({\left | x - 3 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 20, normalized size = 0.80 \begin {gather*} 11 \ln \left (x -3\right )-14 \ln \left (x -2\right )+4 \ln \left (x -1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.07, size = 19, normalized size = 0.76 \begin {gather*} 4 \, \log \left (x - 1\right ) - 14 \, \log \left (x - 2\right ) + 11 \, \log \left (x - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.14, size = 19, normalized size = 0.76 \begin {gather*} 4\,\ln \left (x-1\right )-14\,\ln \left (x-2\right )+11\,\ln \left (x-3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 19, normalized size = 0.76 \begin {gather*} 11 \log {\left (x - 3 \right )} - 14 \log {\left (x - 2 \right )} + 4 \log {\left (x - 1 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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